List questions from solution-verification

Published on 13 Apr 2026 - 4:58

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Proof by contraposition.

Published on 11 Apr 2026 - 20:19

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$\lim\limits_{n \to \infty} \frac{a_n}{b_n}=l$ ; Prove $\sum\limits_{k=1}^\infty a_k$ converges iff $\sum\limits_{k=1}^\infty b_k$ converges.

Published on 14 Apr 2026 - 17:42

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Diagonalizable similar matrices proof

Published on 17 Apr 2026 - 1:18

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If $f(x)\leq g(x)$ for all $x\in [a,b]$ then $\displaystyle \int_a^b f(x)dx\leq \int_a^b g(x)dx$

Published on 17 Apr 2026 - 11:30

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Does $\|T\|=1$ for a unitary operator?

Published on 09 Apr 2026 - 12:17

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How can I show that $\{f\in C([0,1]): d(f,0)\leq 1\}$ is not compact?

Published on 12 Apr 2026 - 9:30

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Is $\{f\in C[0,1]: f(0)=f(1)\}$ a closed subset of $C[0,1]$?

Published on 16 Apr 2026 - 6:16

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Proof of the replacement property of a propositional logic formula.

Published on 10 Apr 2026 - 19:51

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Atiyah-MacDonald 5.16: Geometric interpretation of Noether normalization lemma

Published on 13 Apr 2026 - 13:18

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A result about the separation of a point and a convex closed set

Published on 12 Apr 2026 - 15:55

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Determining the even Fibonacci numbers.

Published on 11 Apr 2026 - 18:41

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Vanishing set of a subset and its minimal ideal are the same.

Published on 14 Apr 2026 - 9:32

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Define X=R\{k} and define ⋆ to be the operation such that x⋆y=(x−k)(y−k)+k. Does this satisfy closure?

Published on 13 Apr 2026 - 23:44

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Consecutive Integer Sum of an m-member Sequence is Divisible by m Proof

Published on 17 Apr 2026 - 9:40

List Question

Equivalent characterizations of discrete valuation rings

Proof by contraposition.

$\lim\limits_{n \to \infty} \frac{a_n}{b_n}=l$ ; Prove $\sum\limits_{k=1}^\infty a_k$ converges iff $\sum\limits_{k=1}^\infty b_k$ converges.

Diagonalizable similar matrices proof

If $f(x)\leq g(x)$ for all $x\in [a,b]$ then $\displaystyle \int_a^b f(x)dx\leq \int_a^b g(x)dx$

Does $\|T\|=1$ for a unitary operator?

How can I show that $\{f\in C([0,1]): d(f,0)\leq 1\}$ is not compact?

Is $\{f\in C[0,1]: f(0)=f(1)\}$ a closed subset of $C[0,1]$?

Proof of the replacement property of a propositional logic formula.

Atiyah-MacDonald 5.16: Geometric interpretation of Noether normalization lemma

A result about the separation of a point and a convex closed set

Determining the even Fibonacci numbers.

Vanishing set of a subset and its minimal ideal are the same.

Define X=R\{k} and define ⋆ to be the operation such that x⋆y=(x−k)(y−k)+k. Does this satisfy closure?

Consecutive Integer Sum of an m-member Sequence is Divisible by m Proof

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